Properties and Numbers 1.4. Deductive Reasoning Using facts, properties or rules to reach a valid conclusion Conjecture: statement that could be true.

Slides:

Advertisements

Similar presentations

Welcome to Interactive Chalkboard

Advertisements

Inductive Reasoning.  Reasoning based on patterns that you observe  Finding the next term in a sequence is a form of inductive reasoning.

Commutative and Associative Properties

Algebraic Properties.

1.4 PROPERTIES OF REAL NUMBERS I CAN IDENTIFY AND USE PROPERTIES OF REAL NUMBERS.

Algebraic Properties: The Rules of Algebra Be Cool - Follow The Rules!

Chapter 1.1 Common Core – A.SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients. Objectives – To write algebraic expressions.

PO D basicadvanced 4b + 6 b= 5, c= 3, d=7 (10c ÷b) 2 + d 4(5) (10(3) ÷5) (30 ÷5) (6)

Algebra 1 Chapter 1 Section Properties of Real Numbers The commutative and associate properties of addition and multiplication allow you to rearrange.

Section 1.1 Inductive Reasoning 1/16. DEDUCTIVE REASONING Two Types of Reasoning INDUCTIVE REASONING 2/16.

Chapter 1-4: Properties Commutative Property: the order in which you add or multiply numbers does not change the sum or product Ex = * 8.

1.7 Logical Reasoning Conditional statements – written in the form If A, then B. Statements in this form are called if-then statements. – Ex. If the popcorn.

Algebra Properties of Real Numbers

Quiz Review Properties and Integers Operations with Decimals Addition Subtraction Multiplication Division.

Operations with Rational Numbers. When simplifying expressions with rational numbers, you must follow the order of operations while remembering your rules.

1-5 Properties and Mental Math I CAN use the commutative and associative properties to add and multiply whole numbers. I CAN use the distributive property.

Commutative Properties The Commutative Property is when a change in the order of the numbers does not change the answer. For example, addition would be:

Chapter 1.  Pg. 4-9  Obj: Learn how to write algebraic expressions.  Content Standard: A.SSE.1.a.

Chapter 2 Section 2-1: Conditional Statements

 I can identify and use the properties of real numbers.

1.2 Inductive Reasoning. Inductive Reasoning If you were to see dark, towering clouds approaching what would you do? Why?

Patterns, Inductive Reasoning & Conjecture. Inductive Reasoning Inductive reasoning is reasoning that is based on patterns you observe.

1-6 Properties of Real Numbers Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

Warm Up (3 + 6) = (4 + 3) a(b – c) = ab – ac = 0 4. (ab)c = (ac)b = 5 6. Name each property Answers 1.Associative property.

Algebra I Sections 2.2, 2.3, 2.5, 2.7. Properties of Addition Commutative Property a + b = b +a a + b = b +a 3 + (-2) = (-2) = Associative.

Over Lesson 1–2 A.A B.B C.C D.D 5-Minute Check 1 A.15 B.11 C.7 D.6 Evaluate the expression c + 8 – a if a = 4 and c = 3. Evaluate the expression 7a –

PROPERTIES OF OPERATIONS Section 5.3. PROPERTIES OF OPERATIONS  The _________ Property states that the order in which numbers are added or multiplied.

Commutative and Associative Properties. Properties are rules in mathematics. You can use math properties to simplify algebraic expressions!

The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

Unit 1, Lesson 6: The Number Properties

5 Minute Check Describe the sequence then find the next three terms. Complete in your notes , 31, 43, 55,… , 64, 50, 36,… , 4.1, 4.8,

Lesson 1-4 Pages Properties Lesson Check 1-3.

Properties of Numbers. Additive Identity Adding “0” to a number gives you the same initial number. Example = = 99.

Properties of Real Numbers

Algebra: Properties Objective: Use communicative, Associative, Identity, and Distributives properties to solve problems. Properties: are statements that.

Ch 2.3 & 2.4 Objective: To solve problems involving operations with integers.

Properties of Equality Properties are rules that allow you to balance, manipulate, and solve equations.

1.4 Properties of Real Numbers ( )

Lesson 1.2 Inductive Reasoning Pages Observe Look for patterns Develop a hypothesis (or conjecture) Test your hypothesis.

Multiplication and Division Properties. Multiplication Properties Commutative Property Associative Property Identity Property Zero Property Distributive.

+ Properties of Real Numbers. + Properties Relationships that are always true fro real numbers are called properties. Properties are rules used to rewrite.

Inductive and Deductive Reasoning Reasoning is used in mathematics, science, and everyday life. When you reach a conclusion, called a generalization,

1-4 Properties How are real-life situations commutative?

Chapter 1 Problem Solving Section 1-1 The Nature of Mathematical Reasoning Objectives: Identify and explain differences between types of reasoning Use.

 Have homework out ready to check.  Ask a neighbor for help if needed!

AND NOT THIS KIND OF EXPRESSION….. Section 1-2 Simplifying Expressions.

How can you use numbers and symbols to represent mathematical ideas?

Properties of Addition and Multiplication

How do you compare and use the properties of real numbers?

CST 24 – Logic.

Properties of Operations

Properties for Addition and Multiplication only

1.7 Logical Reasoning and Counterexamples

Real Numbers and Number Operations

Warm Up Simplify: -18+(-7) (-13)+6 32-(-2) 2-48.

Five step procedure for drawing conclusions.

Patterns and Inductive Reasoning

Equations and Inequalities

Commutative Properties

Real Numbers and their Properties

Properties of Real Numbers

are statements that are true for all numbers.

Properties A property is something that is true for all situations.

Properties of Real Numbers

Properties of Operations

2-1 Inductive Reasoning and Conjecture

Lesson 3 Properties of Operations

video Warm-Up Lesson 11 hw questions?? Lesson 12 Exit card

Presentation transcript:

Properties and Numbers 1.4

Deductive Reasoning Using facts, properties or rules to reach a valid conclusion Conjecture: statement that could be true of false Counter Example: an example that shows a statement is not true.

Ex: State whether each conjecture is true. If not give a counterexample. The sum of an even and an odd number is always even. False: 4+1 =5 which is odd

Commutative Properties: Change Order Addition Rule: Ex: Multiplication Rule: Ex:

Associative Properties: Change Grouping Addition (a+b)+c =a+(b+c) Ex: Multiplication Ex:

Identity Properties Addition (0) Rule: a + 0 = a Ex: = 7 Multiplication(1) Rule: Ex:

Name the Property Example: 4+(a+3)=(a+3) +4 Answer: Commutative because the numbers changed order Example: 1(3c)=3c Answer: Identity Property because you multiplied by 1 and the number did not change

Name the Property Ex: 14+(9+10)=(14+9)+10 Answer: Associative because the grouping symbols changed Ex: d+0 =d Answer: Identity of addition because you added by 0 and the result stayed the same

Simplify the phrase using the properties Ex: 9 +(5+y)

Answer the following 2 questions: 1.) Is division of whole numbers associative? If not give a counterexample 2.) Is subtraction of whole numbers commutative? If not give a counterexample

Homework Page 22 (14-39 all, even)